Computer graphics and visualization and computer aided design and rendering have become very important and useful tools in many and diverse areas of science, technology, engineering, art, architecture, and many other fields.
Surfaces representing three dimensional objects have traditionally been rendered by wireframes, lattices, or by solid colors or shading of various levels of transparency or opacity. There are, however, problems and deficiencies which are inherent with the known techniques for visualization and rendering using wireframe, lattice, solid rendering, etc. Wireframes and lattices, generally given by multiple line segments corresponding to a surface may become confusing as overlapping line segments do not clearly depict depth and may not clearly render a portion of a surface closer to a viewpoint as distinct from a portion of a surface which should appear farther away from a viewpoint. Problems may also exist with solid color or semi-transparent shading rendering of surfaces with nearer portions of a surface partially or totally obscuring more distant portions of a surface.